An algorithm, based on the Equation-free concept, for the
approximation of coarse-grained center manifolds of microscopic
simulators is addressed. It is assumed that the macroscopic
equations describing the emergent dynamics are not available in a
closed form. Appropriately initialized short runs of the microscopic
simulators, which are treated as black box input-output maps
provide a polynomial estimate of a local coarse-grained center
manifold; the coefficients of the polynomial are obtained by
wrapping around the microscopic simulator an optimization algorithm.
The proposed method is demonstrated through kinetic Monte Carlo
simulations, of simple reactions taking place on catalytic surfaces,
exhibiting coarse-grained turning points and Andronov-Hopf
bifurcations.